# Network Recovery from Unlabeled Noisy Samples

arXiv: https://arxiv.org/abs/2104.14952 · HTML: https://mlsanity.com/paper/2104.14952/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Apr 2021.

## Built on by (most cited first, 5 of 5)

- [Nested stochastic block model for simultaneously clustering networks and nodes](https://mlsanity.com/paper/2307.09210/) (2023)
- [Sharp Threshold for the Frechet Mean (or Median) of Inhomogeneous Erdos-Renyi Random Graphs](https://mlsanity.com/paper/2201.11954/) (2022)
- [Estimation of the Sample Frechet Mean: A Convolutional Neural Network Approach](https://mlsanity.com/paper/2210.07401/) (2022)
- [Asymptotically perfect seeded graph matching without edge correlation (and applications to inference)](https://mlsanity.com/paper/2506.02825/) (2025)
- [Graph Convolutional Attention: A Spectral Perspective on Graph Denoising and Diffusion](https://mlsanity.com/paper/2607.06546/) (2026)

## Abstract (arXiv)

There is a growing literature on the statistical analysis of multiple networks in which the network is the fundamental data object. However, most of this work requires networks on a shared set of labeled vertices. In this work, we consider the question of recovering a parent network based on noisy unlabeled samples. We identify a specific regime in the noisy network literature for recovery that is asymptotically unbiased and computationally tractable based on a three-stage recovery procedure: first, we align the networks via a sequential pairwise graph matching procedure; next, we compute the sample average of the aligned networks; finally, we obtain an estimate of the parent by thresholding the sample average. Previous work on multiple unlabeled networks is only possible for trivial networks due to the complexity of brute-force computations.